As introduced in the previous atom, the mole can be used to relate masses of substances to the quantity of atoms therein. The benefit thereof is an easy way of characterizing chemical reactions and determining how much of one substance can react with a given amount of another substance.
From moles of a substance, one can also find the number of atoms in a sample and vice versa. The bridge between atoms and moles is Avogadro's number, 6.022 x 1023.
Avogadro's number is dimensionless, but when it defines the mole, it can be expressed as 6.022 x 1023 mol-1; this form of the number is known as Avogadro's constant. This form shows the role of Avogadro's number as a conversion factor between the number of entities and the number of moles. Therefore, given the relationship 1 mol/6.022 x 1023 atoms, converting between moles and atoms of a substance becomes a simple dimensional analysis problem.
Converting Moles to Atoms
Given a known number of moles (x), one can find the number of atoms in this molar quantity by multiplying it by Avogadro's number:
For example, if we want to know how may atoms are in six moles of sodium, we could solve:
6 moles*(6.022*1023 atoms/mole)=3.61*1024 atoms
Note that the solution is independent of whether the element is sodium or otherwise.
Converting Atoms to Moles
Reversing the calculation above, we can convert a number of atoms to a molar quantity by dividing it by Avogadro's number:
This can be written without a fraction in the denominator by multiplying the number of atoms by the reciprocal of Avogadro's number:
For example, if we know there are 3.5*1024 atoms in a sample, we can calculate the number of moles this quantity represents:
3.5*1024 atoms*(1 mole/6.022*1023 atoms)=5.81 moles